Regarding Florida law, you will need a carseat for the 3 year old but not for the 5 year old.
It's 3 and under in a carseat and ages 4 and 5 need to be in the back seat with a seat belt.
I would bring my own carseat, though, IMHO, because the car rental places can be old and yucky. Also it's approx. $5 a day.